1. On the Optimal SINR in Random Access Networks with Spatial Re-Use Navid Ehsan and R. L. Cruz UCSD

2. On Public Speaking The 85% Rule Should I be talking now? An Analogy…

3. The bottom line, almost… Horizontal throughput (bit meter/sec) versus link reliability

4. Model (“infinite density”) Slotted system, users distributed throughout infinite plane In each slot, the set of transmitting users forms a 2-D Poisson point process with spatial intensity (includes re-transmissions) Each transmission is to a fixed receiver at distance r

5. Model, cont’d Flat fading channel model. Power attenuation between two points separated by distance x is l(x) = (1 + A x) -     path loss exponent,  > 2 A = constant (we later assume A=1)

6. Model, cont’d Each active transmitter transmits with power P Thermal noise power at each receiver is  2 Assume interference from different transmitters are uncorrelated

7. Model, cont’d Total interference from all transmissions at a given receiver at position x: I =  i P l( | y i - x | ) – random sum of received powers – => interference power in each slot is random – approximate I as Gaussian, can get mean and variance of I from Campbell’s theorem

8. Model, cont’d Signal to Interference and Noise Ratio SINR =  = Pl(r ) / (  2 + I ) SINR in each slot is random

9. Model, cont’d Target SINR:  target –If   target then transmission is successful, otherwise it is not successful Information rate:  –  = W log 2 (1 +  target ) (Shannon) –Assumes noise + interference is Gaussian –W = Bandwidth, assume = 1 Hz.

10. Optimization Problem Horizontal Throughput per unit area: – J = max{  r P succ :  r,  target } –P succ = Prob (  >  target ) Theorem

11. Optimal Parameters  * = ,  * = 0,   target =0 (-  dB), P* succ =1, r* = 1/[A(a-1)].  = G, (offered info load per unit area) Optimal load:

12. Finitely Dense Networks Model Location of nodes in each slot is a 2D Poisson point process with intensity 0. Each node transmits with probability / 0 in each slot, so that set of transmitting nodes in each slot is a 2D Poisson point process with intensity. P succ = ( 1 - / 0 )Prob{  >  target } 0 ≤ ≤ 0 ==>  is finite

13. J*( ) as a function of for various values of 0

14. The bottom line… Horizontal throughput (bit meter/sec) versus target SINR 0 = 30

15. Horizontal throughput (bit meter/sec) versus target SINR 0 = 15,60

16. The bottom line, almost… Horizontal throughput (bit meter/sec) versus link reliability

17. Six is a magic number?